Simple & Compound Interest – Ladakh TET Study Notes
(Quantitative Aptitude – Chapter 1.1)
Topic: Simple & Compound Interest
Exam: Ladakh Teacher Eligibility Test (TET) – Quantitative Aptitude
Purpose: Master the concepts, formulas, and calculation techniques to score high on arithmetic questions involving interest.
1. Simple Interest (SI)
1.1 What is Simple Interest?
Simple interest is the interest calculated only on the principal amount, for a given period of time.
1.2 Formula
[ \text{SI} = \frac{P \times R \times T}{100} ]
- P – Principal (initial amount)
- R – Annual rate of interest (in %)
- T – Time period (in years)
1.3 Total Amount (A)
[ A = P + \text{SI} \quad\Rightarrow\quad A = P + \frac{P \times R \times T}{100} ]
2. Compound Interest (CI)
2.1 What is Compound Interest?
Compound interest is interest calculated on the initial principal plus all previously earned interest. The compounding frequency determines how often interest is added.
2.2 General Formula
[ A = P \left(1 + \frac{R}{n \times 100}\right)^{n \times T} ]
- P – Principal
- R – Annual nominal rate of interest (in %)
- n – Number of compounding periods per year
- T – Time period (in years)
The Compound Interest (CI) earned is:
[ \text{CI} = A - P ]
2.3 Special Cases
| Compounding | Formula for A |
|---|---|
| Annual (n = 1) | (A = P(1 + R/100)^{T}) |
| Half‑annual (n = 2) | (A = P(1 + R/200)^{2T}) |
| Quarterly (n = 4) | (A = P(1 + R/400)^{4T}) |
| Monthly (n = 12) | (A = P(1 + R/1200)^{12T}) |
| Daily (n = 365) | (A = P(1 + R/36500)^{365T}) |
Tip: For TET questions, the compounding frequency is usually annual unless explicitly stated.
3. Key Points & Tricks for TET
| Concept | Quick Reminder |
|---|---|
| SI | Directly proportional to (P, R, T). |
| CI | Exponential growth; small changes in (R) or (T) have big effects. |
| Effective Rate | For annual compounding, effective annual rate = nominal rate. |
| Half‑Year vs. Annual | If interest is paid twice a year, use (n=2). |
| Simple vs. Compound | If you’re given a total amount and need to find (P), use the inverse formula. |
| Time in Years | Convert months to years: ( \text{Months}/12 ). |
| Percentage | Always keep R in percent form; divide by 100 in the formula. |
| Rounding | Round only at the final answer. |
| Common Mistakes | Forgetting to divide R by 100, misinterpreting compounding frequency. |
4. Worked Example
Example 1 – Simple Interest
Problem
A sum of ₹12,000 is invested at an annual simple interest rate of 5%. Find the interest earned in 3 years.
Solution
[ \text{SI} = \frac{P \times R \times T}{100} = \frac{12,000 \times 5 \times 3}{100} = \frac{180,000}{100} = 1,800 \text{ ₹} ]
Answer: ₹1,800
Example 2 – Compound Interest
Problem
₹8,000 is deposited in a bank account that pays 6 % per annum compounded quarterly. How much will the account be worth after 4 years?
Solution
-
Identify parameters
- (P = 8,000)
- (R = 6%)
- (n = 4) (quarterly)
- (T = 4) years
-
Apply formula
[ A = 8,000 \left(1 + \frac{6}{4 \times 100}\right)^{4 \times 4} = 8,000 \left(1 + \frac{6}{400}\right)^{16} = 8,000 \left(1 + 0.015\right)^{16} = 8,000 \times (1.015)^{16} ]
- Compute ( (1.015)^{16} )
Use a calculator or successive squaring:
[ (1.015)^{16} \approx 1.26824 ]
- Find (A)
[ A \approx 8,000 \times 1.26824 = 10,145.92 \text{ ₹} ]
Answer: ₹10,145.92 (≈ ₹10,146)
5. Quick Revision Summary
| Topic | Formula | Usage |
|---|---|---|
| Simple Interest | (\text{SI} = \dfrac{P R T}{100}) | Straightforward; use when interest is not compounded. |
| Total Amount (SI) | (A = P + \text{SI}) | For final balance after simple interest. |
| Compound Interest | (A = P\left(1 + \dfrac{R}{n\times100}\right)^{nT}) | Use for compound scenarios. |
| Compounding Frequency | Annual (n=1), Half‑annual (n=2), Quarterly (n=4), Monthly (n=12) | Determine (n) from problem statement. |
| Key Tips | • Keep R in percent form. • Use inverse formulas for missing variables. • Convert time to years when necessary. |
Avoid common pitfalls and save time |